The use of data-based function models is provided for the implementation of function models in control units, in particular engine control units for internal combustion engines. Parameter-free data-based function models are frequently used, since they may be prepared without specific specifications from training data, i.e., a set of training data points.
One example of a data-based function model is represented by the so-called Gaussian process model, which is based on the Gaussian process regression. The Gaussian process regression is a multifaceted method for database modeling of complex physical systems. Regression analysis is typically based on large quantities of training data, so that it is advantageous to use approximate approaches, which may be analyzed more efficiently.
For the Gaussian process model, the possibility exists of a sparse Gaussian process regression, during which only a representative set of supporting point data is used to prepare the data-based function model. For this purpose, the supporting point data must be selected or derived in a suitable way from the training data.
The publications by E. Snelson et al., “Sparse Gaussian Processes using Pseudo-inputs”, 2006 Neural Information Processing Systems 18 (NIPS) and Csató, Lehel; Opper, Manfred, “Sparse On-Line Gaussian Processes”; Neural Computation 14: pages 641-668, 2002, discuss a method for ascertaining supporting point data for a sparse Gaussian process model.
Other methods in this regard are discussed in Smola, A. J., Schölkopf, W., “Sparse Greedy Gaussian Process Regression”, Advances in Neural Information Processing Systems 13, pages 619-625, 2001, and Seeger, M., Williams, C. K., Lawrence, N. D., “Fast-Forward Selection to Speed up Sparse Gaussian Process Regression”, Proceedings of the 9th International Workshop on Artificial Intelligence and Statistics, 2003.
Furthermore, control modules having a main computing unit and a model calculation unit for calculating data-based function models in a control unit are known from the related art. Thus, for example, the publication DE 10 2010 028 259 A1 describes a control unit having an additional logic circuit as a model calculation unit which is configured for calculating exponential functions to assist in carrying out Bayesian regression methods, which are required in particular for calculating Gaussian process models.
The model calculation unit is configured as a whole for carrying out mathematical processes for calculating the data-based function model based on parameters and supporting points or training data. In particular, the functions of the model calculation unit are implemented solely in hardware for efficient calculation of exponential and summation functions, so that it is made possible to calculate Gaussian process models at a higher computing speed than may be carried out in the software-controlled main computing unit.